“You know, Mother Teresa is a saint now, but if Congress wanted to make her a saint, and attach that to the debt ceiling, we probably couldn’t get 218 votes for it,” House Speaker John Boehner told reporters in the Capitol on Thursday.

“Maybe we ought to defund Obamacare—that worked so well for us,” joked Rep. Mike Simpson (R-Idaho). “I’m just kidding.”

“I have as much clarity as anybody else does,” Rep. Patrick McHenry (R-N.C.) said about what House Republicans will demand for their support in lifting the country’s borrowing cap. When asked what he’d personally demand, McHenry joked, “Oh, it doesn’t matter.”

The playful talk underscored a very real problem for Republicans: With the Treasury Department warning the debt ceiling must be raised by the end of February, the party is still stumped about what it wants to try to extract in the latest round of Washington brinksmanship. Republicans abhor the thought of raising the debt limit with no strings attached. But they have struggled to find something that will appease both a large contingent of House Republicans and enough Democrats to pass.

The House Republican leadership has floated attaching a debt-ceiling increase to approval of the controversial Keystone XL Pipeline and repeal of an obscure provision in the health care reform law, but both ideas have gone nowhere in the conference, according to leadership aides. The new flavors of the day on Thursday included a temporary fix to protect doctors who treat Medicare patients from steep cuts to their reimbursement payments, as well as restoring billions of dollars in cuts made to military veterans’ pensions in last year’s budget agreement.

Both issues could theoretically get bipartisan support—depending on the details. But President Barack Obama and Senate Majority Leader Harry Reid remain adamant that the House pass a “clean” debt-limit increase, with no strings attached.

“We shouldn’t be negotiating over the full faith and credit of the United States government,” said Rep. Steve Israel (D-N.Y.), who chairs House Democrats’ campaign arm. While Israel said he couldn’t commit his vote until he sees what Republicans actually propose and that he prefers a clean hike, he allowed that the latest ideas could get bipartisan support “in concept.”

Reps. Hal Rogers (R-Ky.), John Fleming (R-La.), Scott Rigell (R-Va.) and Simpson said they would all support restoring funding for military pensions. Rigell, who represents the largest concentration of military personnel of any congressional district in the nation, said it would “advance a key Republican priority, which is to stand strongly with our men and women in uniform.”

But even while the latest leadership proposals gained some traction, no one was under the illusion that there’s an official party strategy around which to coalesce. As Rep. Aaron Schock (R-Ill.) told TIME: “Anybody who says they know is full of it.”